The disruption of a star by a supermassive black hole generates a sudden bright flare. Previous studies have focused on the disruption by single black holes, for which the fallback rate decays as ∝ t^−5/3. In this paper, we generalize the study to the case of a supermassive black hole binary (SMBHB), using both analytical estimates and hydrodynamical simulations, looking for specific observable signatures. The range of binary separation for which it is possible to distinguish between the disruption created by a single or a binary black hole concerns typically separations of the order of a few milliparsecs for a primary of mass ∼10^6 M_⊙. When the fallback rate is affected by the secondary, it undergoes two types interruptions, depending on the initial inclination θ of the orbit of the star relative to the plane of the SMBHB. For θ ≲ 70°, periodic sharp interruptions occur and the time of first interruption depends on the distance of the secondary black hole with the debris. If θ ≳ 70°, a first smooth interruption occurs, but not always followed by a further recovery of the fallback rate. This implies that most of the TDEs around a SMBHB will undergo periodic sharp interruptions of their light curve.